diff --git a/src/fake-timers-src.js b/src/fake-timers-src.js
index 5741f96..b9a8a8d 100644
--- a/src/fake-timers-src.js
+++ b/src/fake-timers-src.js
@@ -450,7 +450,10 @@ function withGlobal(_global) {
 
                 // ensures identity checks using the constructor prop still works
                 // this should have no other functional effect
-                this.constructor = NativeDate;
+                Object.defineProperty(this, "constructor", {
+                    value: NativeDate,
+                    enumerable: false,
+                });
             }
 
             static [Symbol.hasInstance](instance) {
diff --git a/test/fake-timers-test.js b/test/fake-timers-test.js
index ae3e8c6..0a4b676 100644
--- a/test/fake-timers-test.js
+++ b/test/fake-timers-test.js
@@ -3212,6 +3212,12 @@ describe("FakeTimers", function () {
             assert.equals(date.constructor, realDate.constructor);
         });
 
+        it("creates Date objects where the constructor prop is not enumerable", function () {
+            const date = new this.clock.Date();
+
+            assert.equals(Object.keys(date).length, 0);
+        });
+
         it("creates Date objects representing clock time", function () {
             const date = new this.clock.Date();